A method is developed for the Bayesian analysis of rate ratios of repeated events in matched cluster-randomized trials, and applied to the Flies and Eyes trial against trachoma in The Gambia. A non-mechanistic analysis estimates the incidence rate ratio for insecticide spray, relative to no intervention, as 0.59 (95 per cent credible interval 0.37--0.92), and for latrine provision as 0.67 (0.41--1.01). The method also yields incidence and clearance rate ratios for age. In the Flies and Eyes trial, the former rates are estimated to decrease with age, although no clear pattern is seen in the latter. Using clinical active trachoma as a marker of infection, and net catches to measure fly density, a mechanistic model is developed to estimate the proportion of transmission due to flies. However, it was not possible to estimate this proportion accurately, and a lack of association was noted between the magnitudes of reductions in fly density and in trachoma. The lack of knowledge on the relative importance of different transmission routes is a constraint on the current global programme for the elimination of trachoma.